SIGNAL FILTERING AND FREQUENCY DOMAIN NOISE BASIC INFORMATION

Effect of Filtering on Signals

As we have seen, many signals have a
bandwidth that is theoretically infinite. Limiting the frequency response of a
channel removes some of the frequency components and causes the time-domain
representation to be distorted.

An uneven frequency response will emphasize
some components at the expense of others, again causing distortion. Nonlinear
phase shift will also affect the time-domain representation.

For instance, shifting the phase angles of
some of the frequency components in the square-wave representation changed the
signal to something other than a square wave. However, while an infinite
bandwidth may theoretically be required, for practical purposes quite a good
representation of a square wave can be obtained with a band-limited signal.

In general, the wider the bandwidth, the
better, but acceptable results can be obtained with a band-limited signal. This
is welcome news, because practical systems always have finite bandwidth.

Noise in the Frequency Domain

Noise power is proportional to bandwidth.
That implies that there is equal noise power in each hertz of bandwidth.
Sometimes this kind of noise is called white noise, since it contains all
frequencies just as white light contains all colors.

In fact, we can talk about a noise power
density in watts per hertz of bandwidth. The equation for this is very simply
derived. We start with Equation (1.3):

PN = kTB

This gives the total noise power in
bandwidth, B. To find the power per hertz, we just divide by the bandwidth to
get an even simpler equation:

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